Questions

  1. How do species differ in their drought response to variable intensity and their recovery patterns?
  2. If species differ, do they also vary regionally? For which species?
  3. Are drought response and recovery mediated by competition and tree size and is this a species specific phenomenon or does it also vary regionally?

Methods

I collected tree ring data from 4 regions across California and performed analyses on detrended growth during drought years where water availability (SPEI) was in the bottom 15th percentile. All tree ring series were spline detrended.

Key responses

\[ Growth Reduction = \frac{\overline{RWI}_{non-drought} - RWI_{drought}}{\overline{RWI}_{non-drought}} \] \[ Recovery = RWI_{actual} - RWI_{pred} \]

Where \(RWI_{pred}\) is the predicted growth for a tree given the post-drought year conditions based on hierarchical Bayesian models of all growth years.

Modeling approach

This approach differs in that here we explore the results of the full expression of the model to answer the above questions i.e. the most complex justifiable model. Each species is modeled independently. This approach is a way to avoid the model selection issues we discussed regarding the complexity of question 3.

\[ Reduction_i \sim Normal(\mu_i, \sigma_i) \]

\[ \mu_i = \alpha_{region_i} + \alpha_{treeID} + \beta_{1region_i}SPEI_i + \beta_{2region_i}DBH_i + \beta_{3region_i}log(hegyi)_i + \beta_{4}SPEI_i\times DBH_i + \beta_{5}SPEI_i \times log(hegyi)_i \]

and for recovery:

\[ Recovery_i \sim Normal(\mu_i, \sigma_i) \]

\[ \mu_i = \alpha_{region_i} + \alpha_{treeID} + \beta_{1region_i}Reduction_i + \beta_{2region_i}DBH_i + \beta_{3region_i}log(hegyi)_i + \beta_{4}Reduction_i\times DBH_i + \beta_{5}Reduction_i \times log(hegyi)_i \]

Does it make sense for DBH, comp, and interactions to vary regionally? What does this mean? Regionally varying responses to drought intensity or severity could reflect local adaptation.

Descriptions of interaction terms

\(SPEI \times DBH\) smaller or larger trees experience the same drought intensity differently. Perhaps this is due to differences in evaporative demand, root:shoot allocation patterns, height water relationship

\(Reduction \times DBH\) smaller or larger trees recover from equally damaging droughts differently. Potentially due to access to resources, allocation again.

\(SPEI \times log(hegyi)\) sparse or dense neighborhoods modify the effect of drought intensity. This could be via resource (water) competition. Although because we lack good characterization of the between neighborhood microsite differences density could reflect suitability more than competition.

\(Reduction \times log(hegyi)\) sparse or dense neighborhoods modify the recovery of trees from equally damaging droughts. This could also be via resource competition although more than just water. Again, patterns may reflect uncharacterized microsite differences rather than competition.

Details

All models converged Rhat ~1 and each model had few divergent samples. Param estimates and plots were prepared with tidybayes. Marginal effects plots were produced with add_fitted_draws() setting re_formula = ~(spei12 + DBH + comp | Region)) excluding (1 | tree.uniqueID).

Results

Q1

Growth Reduction

Table SX. Growth reduction WAIC table
waic_diff se
SPEI only 0.00000 0.000000
Species + SPEI 2.04252 3.076878
Species * SPEI 4.74648 3.720620
Table SX. Growth reduction variance contrasts
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
PJ - AC > 0 0.0666103 0.0096405 0.0505275 0.0820601 Inf 1.0000
PL - AC > 0 0.0342796 0.0118112 0.0155830 0.0540833 9.9900e+02 0.9990
PL - PJ > 0 -0.1272120 0.0475280 -0.2065795 -0.0489364 5.5304e-03 0.0055
Table SX. Growth reduction intercept contrasts
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
PJ - AC > 0 0.0205816 0.0136596 -0.0024442 0.0429330 14.094340 0.93375
PL - AC > 0 0.0103469 0.0157787 -0.0155560 0.0364456 2.906250 0.74400
PL - PJ > 0 -0.0102347 0.0161652 -0.0368797 0.0164271 0.356392 0.26275

Recovery

Table SX. Recovery WAIC table
waic_diff se
Varying intercept and slope 0.000000 0.00000
Varying intercept 4.186948 10.25373
No species effect 12.834264 12.04065
Table SX. Recovery variance contrasts
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
PJ - AC > 0 0.0551883 0.0086157 0.0409969 0.0693746 Inf 1.00000
PL - AC > 0 0.0358049 0.0107017 0.0183191 0.0538784 3.99900e+03 0.99975
PL - PJ > 0 -0.0891320 0.0502752 -0.1715589 -0.0051960 4.32968e-02 0.04150
Table SX. Recovery intercept contrasts
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
PJ - AC > 0 0.0315932 0.0175444 0.0029861 0.0603802 27.98551 0.96550
PL - AC > 0 0.0967908 0.0224670 0.0598268 0.1338717 Inf 1.00000
PL - PJ > 0 0.0651976 0.0225358 0.0287279 0.1016507 1332.33333 0.99925
Table SX. Recovery slope contrasts
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
PJ - AC > 0 -0.0809188 0.0411304 -0.1481597 -0.0133473 0.025641 0.02500
PL - AC > 0 0.0800334 0.0534826 -0.0074203 0.1685892 14.094340 0.93375
PL - PJ > 0 0.1609522 0.0511764 0.0771802 0.2447245 1332.333333 0.99925

Main Figure

Q2

Growth Reduction

Regional differences are crucial to dtermining growth reduction. Across all species at least two sites are significantly different from one another in intercept and spei slope. The site patterns across species are qualitatively consistent which is in line with the model selection supporting modeling all of the species together.

Table SX. A. concolor growth reduction WAIC table
waic_diff se
Varying intercept and slope 0.00000 0.00000
No regional effects 43.30953 12.80732
Varying intercept 45.11601 12.72891
Table SX. P. jeffreyi growth reduction WAIC table
waic_diff se
Varying intercept and slope 0.00000 0.00000
Varying intercept 41.83552 12.88420
No regional effects 43.82051 13.91644
Table SX. P. lambertiana growth reduction WAIC table
waic_diff se
Varying intercept and slope 0.00000 0.000000
No regional effects 18.41681 7.836080
Varying intercept 19.29546 7.449942

Recovery

Regional effects appear to be less important for recovery as none of the intercepts growth reduction slopes for any sites are significantly different from one another. Note that these results differ from the simpler model as the CI are wider here (see other md).

Table SX. A. concolor recovery WAIC table
waic_diff se
Varying intercept and slope 0.000000 0.000000
Varying intercept 1.851447 5.964911
No regional effects 12.912958 9.351119
Table SX. P. jeffreyi recovery WAIC table
waic_diff se
Varying intercept and slope 0.000000 0.000000
Varying intercept 7.988191 8.352711
No regional effects 22.441717 12.987328
Table SX. P. lambertiana recovery WAIC table
waic_diff se
Varying intercept and slope 0.000000 0.000000
Varying intercept 4.836886 8.154183
No regional effects 36.244175 11.872226

Main Figure

Table SX. ICC for regionally varying parameters (AC, growth reduction)
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
region intercept/total 0.5970135 0.1336668 0.3013006 0.8868626 NA NA
region slope/total 0.2677814 0.1137323 0.0737678 0.5785439 NA NA
Table SX. ICC for regionally varying parameters (PJ, growth reduction)
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
region intercept/total 0.5486569 0.1608815 0.2163339 0.8879885 NA NA
region slope/total 0.2554130 0.1337445 0.0574560 0.6456691 NA NA
Table SX. ICC for regionally varying parameters (PL, growth reduction)
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
region intercept/total 0.4047434 0.3123458 0.0035201 0.9735754 NA NA
region slope/total 0.4766134 0.3515581 0.0141206 0.9946826 NA NA
Table SX. ICC for regionally varying parameters (AC, recovery)
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
region intercept/total 0.2333188 0.2132561 0.0152736 0.8137307 NA NA
region slope/total 0.3221096 0.2583555 0.0039577 0.8943126 NA NA
Table SX. ICC for regionally varying parameters (PJ, recovery)
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
region intercept/total 0.1958702 0.2089063 0.0081197 0.8032205 NA NA
region slope/total 0.3258525 0.2541065 0.0158146 0.9298125 NA NA
Table SX. ICC for regionally varying parameters (PL, recovery)
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
region intercept/total 0.2531975 0.2850897 0.0014873 0.9548398 NA NA
region slope/total 0.5320250 0.3267092 0.0123234 0.9933452 NA NA

Median and 95% CI growth reduction regression coefficients for a) white fir, b) jeffrey pine, and c) sugar pine as well as recovery regression coefficients for d) white fir, e) jeffrey pine, and f) sugar pine.

Q3

Main Figure

Growth Reduction

DBH, competition and their interaction with spei are surprisingly of little effect with the exception of the importance of DBH and its interaction with spei for Jeffrey pine where larger trees fare worse in more severe droughts.

Keep in mind that in the scatter plots the drought intensity axis is flipped, so slope will appear to be wrong sign from the parameter estimate plots.

Recovery

Recovery shows some evidence that tree and stand characteristics are important to the overall drought response. White fir recovery is impacted by DBH, although this does not vary dramatically region to region. Recovery in two out of four populations of jeffrey pine are affected by competition through the interaction with growth reduction. In these locations recovery from episodes that result in growth reductions is better in dense areas and worse in areas with lower competition (potential microsite signal as mentioned earlier). Sugar pine in the two southern regions appears to be dependent on DBH and competition; larger trees and trees in more dense neighborhoods have better recovery.